How do you solve #a/15=4/5#?

4 Answers
Mar 27, 2018

Answer:

#color(teal)(a=12#

Explanation:

Simply use cross multiplication #...#
#color(teal)(a/15=4/5#

#or, # #color(teal)(5a=4*15#

#or, # #color(teal)(a=(4*15)/5=4*3=12#

hope that helped.

Mar 27, 2018

Answer:

a = 12

Explanation:

Here, #a/15 = 4/5#
Or,#5*a# = #15*4#
Or,5a = 60
Or,a = #60/5#
Or,a = 12

Mar 27, 2018

Answer:

#a=12#

Explanation:

#"Alternatively multiply both sides of the equation by"#
#"the "color(blue)"lowest common multiple of 15 and 5"#

#"the lowest common multiple of 15 and 5 is 15"#

#cancel(15)^1xxa/cancel(15)^1=cancel(15)^3xx4/cancel(5)^1#

#rArra=3xx4=12#

Mar 27, 2018

Answer:

#a=12#

Explanation:

#color(blue)("Important fact")#

A fraction's structure is such that we have:

#("numerators")/("denominators") color(white)("d")->color(white)("dd") ("count")/("size indicator of what is being counted")#

You can not #color(purple)(ul("DIRECTLY"))# add, subtract or compare the 'counts' unless the 'size indicators' are the same.

Multiply by 1 and you do not change the value of something. However, 1 comes in many forms so you change the way something looks without changing its value.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Answering the question")#

#color(green)(a/15=[4/5color(red)(xx1)] color(white)("dddd")->color(white)("dddd")a/15=[4/5color(red)(xx3/3) ])#

#color(green)(color(white)("dddddddddddddddd")->color(white)("dddd")a/15=12/15)#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Now that the bottom numbers or size indicators (denominators) are the same we can just compare the top numbers or counts (numerators).

Mathematically you say: multiply both sides by 15#

So we now have: #a=12#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Check")#

If we divide the left hand side by the right hand side we will get 1 if they are the same.

#12/15-:4/5#

#12/15xx5/4 #

# 5/15xx12/4 #

#1/3xx3/1=1#